RATES OF INCREASE IN DOLPHIN POPULATION SIZE 



Stephen B. Reilly and Jay Barlow 1 



ABSTRACT 



Annual finite rates of increase in dolphin population size were estimated to vary up to a maximum of 

 1.09, using simulation, based on ranges in vital rates. Vital rate ranges were defined from values reported 

 in the literature where possible, otherwise by making assumptions about biological or logical limits. Given 

 information on current values, or limits, of one or more vital rate, one can use the figures presented 

 to determine ranges of possible rates of increase in population size. The highest rates estimated here 

 (up to 1 .09) are probably unrealistic, because of the unlikely combinations of high fecundity and low mor- 

 tality needed to achieve them. 



Rates of increase in population size are important 

 in determining management strategies for fish and 

 wildlife subject to exploitation. A common manage- 

 ment approach for setting incidental mortality or 

 harvest quotas is to use a stock-production model 

 (Schaeffer 1957; Allen 1976) with an assumed max- 

 imum rate of increase. For dolphins and other ceta- 

 ceans, rates of increase have proven extremely dif- 

 ficult to measure directly. Nonetheless, estimates 

 of this parameter are sometimes necessary, e.g., in 

 setting incidental mortality quotas for dolphin 

 populations involved in the eastern tropical Pacific 

 purse seine fishery for yellowfin tuna (Smith 1983). 

 In such situations, even a range, when rigorously 

 defined, can contribute substantially to delineating 

 the management options. 



In this paper we define a range of reasonable 

 values of rate of increase (hereafter also referred 

 to as ROI) in dolphin population size, given what is 

 known or can be inferred about their age-specific 

 survival and fecundity distributions, or "vital rates". 

 We estimate rates of increase using population pro- 

 jection matrices for various parameter combina- 

 tions. We also suggest how the resulting ranges in 

 ROI can be further narrowed, given specific infor- 

 mation for an individual population. 



There are many slightly different definitions for 

 rate of increase, but all share the commonsense no- 

 tion of change in population size over time. Caughley 

 (1977) reiterated the distinction between exponen- 

 tial and finite rates: finite rates, here symbolized A, 

 are related to exponential rates, here symbolized r, 

 by the simple conversion A = e r . (We use the term 



Southwest Fisheries Center La Jolla Laboratory, National 

 Marine Fisheries Service, NOAA, P.O. Box 271, La Jolla, CA 

 92038. 



"finite rates of increase" for A following Birch 1948.) 

 Further, within exponential rates Caughley distin- 

 guished among "intrinsic" (r m ), "survival-fecun- 

 dity" (r s ) and "observed" (r), rates. 



In this paper we compute a series of r s values, 

 resulting from ranges of survival-fecundity distribu- 

 tions. The highest value of r s resulting from the 

 range of vital rates considered is our best estimate 

 of dolphin r m , or "r-max". 



We define the ranges in vital rates based on the 

 literature for dolphins where possible. Otherwise, 

 we rely on information for other large mammals and 

 what appear to be logical or biological limits. 



There are two previous studies of a similar nature 

 for delphinids. As part of a general review of life 

 history analysis of large mammals, Goodman (1981) 

 examined the relationships among rate of increase, 

 juvenile and adult survival rates. He looked at single 

 values for calving interval and age at first reproduc- 

 tion across ranges of survival rates. We take a 

 broader look at these relationships, examining 

 ranges for all four parameters. 



Polacheck (1984) examined interparameter rela- 

 tionships for eastern tropical Pacific (ETP) dolphins, 

 Stenella spp., given specific vital rate estimates 

 available as of 1981, showing the values were not 

 consistent with a positive population growth rate. 

 Since then, revised estimates have become available 

 for some relevant parameters, and this specific case 

 has been reanalyzed, with similar general conclu- 

 sions. 



The only reported dolphin rates of increase are 

 for Stenella coeruleoalba. For the year 1974, Kasuya 

 (1976) estimated a rate of 0.024 for the population 

 off Japan. This value was computed in a complex 

 manner, based on an observed fishing mortality, 

 assumed natural mortality, and estimated popula- 



Manuscript accepted October 1985. 

 FISHERY BULLETIN: VOL. 84, NO. 3, 1986. 



527 



